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timezone-relative day count for Mars
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by Andrew Main (Zefram)
2007-02-17
abstract
--------
Terran calendarists have found a need for a timezone-relative version of
astronomers' absolute day count systems, and have defined such systems.
The same need exists in Martian timekeeping. An absolute day count for
Mars exists in the form of the Mars Sol Date (MSD), but there appears to
be no established convention for a timezone-relative day count for Mars.
This memo therefore defines the Chronological Mars Solar Date (CMSD),
with the equation CMSD = MSD + 500000 + Zoff, where Zoff is the timezone
offset in fractional days. Related quantities are also defined.
table of contents
-----------------
0. need
0.0. Terra
0.1. Mars
1. definitions
2. references
0. need
=======
0.0. Terra
----------
In situations where calendars are a distraction, such as astronomy,
it is often preferred to track time by a simple linear count of days
elapsed since a well-known epoch. For example, the Julian Date (JD) is
defined as the number of days elapsed since -4713-11-24T12 UT (proleptic
Gregorian calendar). JD and its derivatives are widely used in scientific
disciplines related to astronomy and timekeeping.
Calendarists and historians have a similar requirement, differing in
an important detail. It is useful to them to express civil dates in a
calendar-neutral manner, in the form of a linear count of days. Civil
dates are usually relative to local solar time, or since the nineteenth
century relative to a locally-mandated timezone. A timezone-relative
day count allows comparison of civil dates across timezones (as opposed
to comparing absolute points in time), and allows a date to be expressed
when its timezone is unknown.
An example of a timezone-relative day count system is the Chronological
Julian Date, described in [JDN] and [CJD-MSG]. It is defined, for any
particular timezone, by the equation
CJD = JD + 0.5 + Zoff
where Zoff is the offset of the timezone's time of day from the UT time
of day, expressed in fractional days.
0.1. Mars
---------
As the study of the planet Mars has progressed, a need to track Martian
solar time has developed. Lander missions, particularly, are affected
by the diurnal cycle, for reasons of visibility and the availability of
solar power. Among those who must deal with Martian and Terran days at
the same time, Martian days are referred to as "sols".
A prime meridian has been defined for Mars, passing through the centre
of the small crater Airy-0 in Meridiani Planum [AIRY-0]. Mean solar
time on the Martian prime meridian is known as Airy Mean Time (AMT), by
analogy with Greenwich Mean Time (GMT), or misleadingly as Coordinated
Mars Time (MTC), by faulty analogy with Coordinated Universal Time (UTC)
[MARS24-TN].
A Martian solar day count has been defined: the Mars Sol-Date (MSD)
[RECIPE]. The MSD is a count of Martian solar days since approximately
JD 2405521.00 in Terrestrial Time, the epoch being chosen for the
near-coincidence of Airy mean midnight with Greenwich mean noon. The MSD
takes an integral value at each mean midnight on the Airy meridian.
Martian lander missions have adopted the Terran civil convention of
referring to local mean solar time, rather than using a single time scale
(AMT) at all longitudes. In fact, the rovers Spirit and Opportunity have
notably not used precisely mean solar time at any point in the immediate
vicinity of the landing site or anticipated operational areas. Rather,
they have adopted the mean solar time of a nearby longitude, chosen to
closely match the apparent solar time of the landing site at the middle
of the nominal mission period [MARS24-TN].
The Mars Exploration Rover missions are thus using timezones. They also
identify each Martian day by an integral number, incrementing uniformly,
with the day of landing identified as "sol 1" [MARS24-TN]. The days
identified by these numbers extend from midnight to midnight in the
mission timezone, and are not tied to AMT. The day counts are not
aligned with each other; they are established separately for each lander.
These lander mission day counts each have the semantics of a
timezone-relative integral day count, analogous to the Chronological
Julian Day Number (CJDN) for Terra. Comparison of dates between missions
would be facilitated by using a single epoch for all missions.
In anticipation of the need for seasonal timekeeping on Mars, there
have been several proposals for calendars to reconcile the Martian day
with the Martian tropical year [CALENDARS]. In fact such a need already
exists: the rover missions are affected by the variable availability of
solar power over the course of the year. As on Terra, the definition
and comparison of calendars would be facilitated by a calendar-neutral
timezone-relative linear day count.
No such timezone-relative day count appears to exist for Mars, except
for the various mission-specific counts used with landers.
1. definitions
==============
The Chronological Mars Solar Date (CMSD) is defined, for any particular
timezone, by the equation
CMSD = MSD + 500000.0 + Zoff
where Zoff is the offset of the timezone's time of day from the AMT time
of day, expressed in fractional days. The constant offset of 500000
is included so that CMSD and MSD values are unlikely to be mistaken for
each other: any such confusion would result in dates almost 750 Martian
years wrong, which should be quickly noticed.
Example (all numbers approximate): the Opportunity rover mission uses
a timezone of AMT-01:01, and so has Zoff = -0.042. The rover landed
in Meridiani Planum at MSD 46236.600. The landing time can thus be
expressed as CMSD 546236.558 in the mission timezone.
The CMSD may be separated into integral and fractional parts.
The integer part is the Chronological Mars Solar Day Number (CMSDN),
and the fractional part is the Chronological Mars Solar Day Fraction
(CMSDF). They are related by the equation
CMSD = CMSDN + CMSDF
where CMSDN is constrained to be an integer and CMSDF is constrained to
be in the range [0, 1).
Example: Opportunity's landing occurred on CMSDN 546236 in the mission
timezone. That is labelled as "sol 1" in the context of the mission,
so the mission sol number can be defined as CMSDN - 546235. The time of
day of the landing was CMSDF 0.558 in the mission timezone, corresponding
to 13:23 on the 24-hour clock. (Time of day approximate.)
2. references
=============
[AIRY-0] Malin Space Science Systems, "The Martian Prime Meridian
-- Longitude "Zero"", MGS MOC Release No. MOC2-273,
31 January 2001, .
[CALENDARS] Thomas Gangale, "Martian Calendars", .
[CJD-MSG] Peter Meyer, "Message Concerning Chronological Julian
Days/Dates", 23 Jan 2004, .
[JDN] Peter Meyer, "Julian Day Numbers", .
[MARS24-TN] Michael Allison and Robert Schmunk, "Technical Notes on Mars
Solar Time as Adopted by the Mars24 Sunclock", Dec. 13 2005,
.
[RECIPE] Michael Allison and Megan McEwen, "A post-Pathfinder
evaluation of aerocentric solar coordinates with
improved timing recipes for Mars seasonal/diurnal climate
studies", 16 August 1999, Planetary and Space Science 48
(2000), 215-235, .